Golf club head with optimized moi and/or roll radius

ABSTRACT

A golf club head with moments of inertia that are optimized about principal axes of the club head. The club head can have a roll radius about its ball striking face that is decreased above a first axis, and increased below the first axis, the first axis being correlated with the principal axes of the club head.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority from U.S. Provisional Patent Application No. 61/513,501, filed Jul. 29, 2011, the contents of which are hereby incorporated by reference in their entirety.

FIELD OF THE INVENTION

This application generally relates to golf club heads, and more specifically to golf clubs having optimized moments of inertia about principal axes and/or vertical roll about the club head face.

BACKGROUND

When a golfer makes a shot, they want the golf ball to travel an intended distance in an intended direction. Golf clubs are generally designed so that best performance is achieved when the club makes contact with the ball near the center of the strike face. However, when a golfer makes an off-center hit, they often find that the ball does not travel far enough or in the desired direction.

Club designers have sought to optimize club performance by manipulating factors such as loft, lie, face size, bulge, roll, center of gravity, moment of inertia, and overall head weight. Despite these efforts, golfers still find that off-center hits can get poor distance and travel in the wrong direction.

SUMMARY

The invention provides a club head in which moments of inertia and face curvature are optimized based on actual hit patterns obtained when golfers play golf. Club heads are provided that have a high moment of inertia along axes of actual hit patterns. Since the moment of inertia causes the club to resist twisting around a center of percussion within the plane defined by a majority of a golfer's off-center hits, the club is forgiving to off-center hits, in a heel-toe direction, in ways that prior art clubs were not. Since the face curvature is oriented in a non-horizontal way based on actual hit patterns, the club is forgiving to off-center hits, in a crown-sole direction, in a way that prior art clubs were not.

An aspect of at least one of the embodiments described herein includes the realization that club heads, particularly wood-type club heads, tend to rotate about axes other than the vertical and horizontal axes during a golf swing. These “principal axes” have been found to relate generally to a golfer's hit pattern on the club head, and have further been found to be tilted at an angle relative to a horizontal and vertical axis extending through the club head. Typically, club heads have moments of inertia that are optimized about the vertical or horizontal axes. However, in order to improve distance, accuracy, and repeatability during a club head swing, it would be advantageous instead to optimize the moments of inertia about the principal axes, so as to limit rotational movement of the club head about the principal axes during the swing.

Another aspect of at least one of the embodiments described herein includes the realization that golf clubs typically have a vertical roll radius about the ball striking face that remains the same moving from the crown of the club head down towards the sole of the club head. This generally constant vertical roll radius can lead to poor results if a golf ball is not struck accurately. Therefore, it would be advantageous to have a club head that includes a vertical roll radius along the ball striking face optimized to give the club head greater ball striking distance regardless of where the ball is hit on the face, as compared with a club head with a constant vertical roll radius.

Overall, it would be advantageous to optimize both the vertical roll radius and the moments of inertia about the principal axes at the same time, thereby facilitating a club head that is designed specifically with a golfer's hit pattern in mind. Such a club head could resist rotational movement about the principal axes, as well as generate optimal ball strikes based on a hit pattern.

In certain aspects, the invention provides a golf club head having a hosel, a strike face, and a body wall defining a hollow body substantially enclosing an inner volume. The body wall includes a weighted area with a mass per unit area greater than an overall mass per unit area of the body wall. The weighted area is within a distance D of about 3 cm from a plane P that intersects the strike face, a toe side of a crown of the body, and a heel side of a sole of the body.

In some embodiments, a crown portion of the strike face is more curved than a sole portion of the strike face. Curvature of the strike face can be defined by making reference to a loft line normal to and passing through a geometric center of the strike face, a reference line through a club head center of gravity and parallel to the loft line, and a measuring line on a surface of the strike face comprising a series of evenly spaced points. The face may be curved such that N surface normals, each normal to and extending from the strike face at one of the points and each defining an angle θ_(N) with the next, provide a θ_(i) above the reference line that is larger than a θ_(j) beneath the reference line. Curvature known as roll radius is thus defined, for example, where the measuring line intersects the reference line and a vertical plane.

In certain embodiments, the plane P intersects a horizontal plane to define an angle between about 20° and about 40° when the club is at address. The plain P may intersect the strike face within about 2 cm of a center of percussion, may intersect the body within about 2 cm of an aft-most point on the club head, or both. The distance D can be smaller, for example, 1 cm (or 2 or 0.5). The weighted portion of the body can be provided by weight member (e.g., fixed to the body wall) or by a joining seam between a crown component and a sole component of the body wall. The seam can provided weight by being filled (e.g., with a filler material) or by being bulky (e.g., comprising two flange portions sealed together to define a 2-ply region and further being optionally folded back on itself to create a 4-ply or greater region).

In certain aspects, the invention provides a golf club head having a body with a hosel and a strike face. The golf club head has a higher moment of inertia about an axis that is perpendicular to a major axis of a hit pattern. Specifically, the club head has a moment of inertia I_(A) about an axis A greater than a moment of inertia I_(Z) about an axis Z, wherein Z is vertical when the club is at address and Z and A form a non-zero angle θ_(A). For example, the angle θ_(A) can be between about 5° and about 45°. The club head tends to diminish hook or slice associated with off-center hits, since the moment of inertia I_(A) resists rotation or twisting around a center of percussion of a hit. Club heads of the invention may further have two different roll radii on a strike face. In some embodiments, a roll radius near a sole is larger than a roll radius near a crown. Further, the two roll radii may be separated by an area of the strike face that is flat—i.e., having no roll radius. The line or area of separation between the crown-side roll radius and the sole-side roll radius may be horizontal across the strike face when the club is at address. In some embodiments, the line or area of separation between the crown-side roll radius and the sole-side roll radius is non-horizontal and may be parallel to an axis B. In certain embodiments, one of the roll radii is between about 200 mm and about 250 mm and the other roll radius R2 is between about 250 mm and about 800 mm.

Further, the club head may have a moment of inertia T_(B) about an axis B greater than a moment of inertia T_(y) about an axis Y, wherein Y is horizontal and extends through a heel side of the club head and a toe side of the club head when the club is at address and B and Y form a non-zero angle θ_(B), and further wherein I_(B) is greater than I_(Y). Angle θ_(B) may be greater than about 15°, e.g., between about 25° and about 30°.

Thus, a club head of the present invention provides an optimized combination of MOI and roll radius, particularly tending to be most forgiving to off-center hits. Further, in certain embodiments, a moment of inertia is optimized through the use of construction seams provided where components of a club head are joined to one another, thus making for a cost effective approach to manufacturing that produces a club head in which mass is distributed evenly in a most optimum pattern.

In certain aspects, the invention provides a golf club head having a ball striking face that includes a geometric center point on a surface of the ball striking face, generally equidistantly from an uppermost portion of the ball striking face and a lowermost portion, as well as equidistantly from a heel and toe end of the ball striking face. When the club is at address, there exists an idealized a vertical axis through the geometric center point and an idealized horizontal axis extending through the geometric center point and angled at zero degrees relative to the address position when the club head is neither open nor closed at address (i.e., the idealized horizontal axis is perpendicular to both the vertical axis and an intended direction of travel of a golf ball). The club head has a hitting zone defined by an anticipated or measured area on the ball striking face where a majority of a golfer's hits typically occur, the hitting zone having generally an elliptical shape angled upwardly from a heel side of the club head to a toe side of the club head. The club head is further describable with reference to a major axis extending through the elliptical hitting zone, the major axis defining a first principal axis of the club head, the major axis being tilted at a non-zero angle relative to the horizontal axis, and a minor axis extending perpendicular to the major axis, the minor axis defining a second principal axis of the club head, the minor axis tilted at the non-zero angle relative to the vertical axis. The club head has a moment of inertia about the major axis that is greater than a moment of inertia of the club head about the horizontal axis. Additionally, the club head may have a moment of inertia about a minor axis that is greater than a moment of inertia about a vertical axis. Further, the club head may include a first roll radius and a larger second roll radius.

In some embodiments, the club head includes a loft line extending through the geometric center point, the loft line perpendicular to the ball striking face at the geometric center point, a center of gravity, and a reference line extending through the center of gravity and the ball striking face, parallel to the loft line. The first roll radius is above a point where the reference line intersects the ball striking face, while the second roll radius is beneath that point.

The hitting zone, being defined by an anticipated or measured area on the ball striking face where a majority of a golfer's hits typically occur, may include hit-points of at least about 90 percent of a golfer's shots. In certain embodiments, the first major axis includes a principal axis of the club head. The major axis may be tilted, relative to the horizontal axis, at a non-zero angle that is between approximately 3.0 and 16.0 degrees

In some embodiments, the first roll radius gives the ball striking face a rounded appearance when viewed from a side, and the second roll radius gives the ball striking face a generally flattened appearance when viewed from the side.

Further, in accordance with at least one embodiment, a golf club head can comprise a ball striking face comprising a geometric center point located on a surface of the ball striking face, the geometric center point located generally equidistantly from an uppermost portion of the ball striking face and a lowermost portion of the ball striking face, as well as equidistantly from a heel and toe end of the ball striking face, a vertical axis comprising an axis that extends through the geometric center point, the vertical axis oriented vertically relative to a flat playing or ground surface when the club head is at an address position, a horizontal axis extending through the geometric center point, the horizontal axis perpendicular to the vertical axis and extending horizontally and generally parallel relative to the flat playing or ground surface, the horizontal axis comprising an axis that is angled at zero degrees relative to the address position when the club head is neither open nor closed at address, a hitting zone defined by an anticipated or measured area on the ball striking face where a majority of a golfer's hits typically occur, the hitting zone having generally an elliptical shape angled upwardly from a heel side of the club head to a toe side of the club head, a major axis extending through the elliptical hitting zone, the major axis defining a first principal axis of the club head, the major axis being tilted at a non-zero angle relative to the horizontal axis, a minor axis extending perpendicular to the major axis, the minor axis defining a second principal axis of the club head, the minor axis tilted at the non-zero angle relative to the vertical axis, wherein a moment of inertia of the club head about the major axis is greater than a moment of inertia of the club head about the horizontal axis, and wherein the club head further comprises a first roll radius above the major axis, and a second roll radius below the major axis, the first roll radius smaller than the second roll radius.

In accordance with at least another embodiment, a golf club head can comprise a ball striking face comprising a geometric center point located on a surface of the ball striking face, the geometric center point located generally equidistantly from an uppermost portion of the ball striking face and a lowermost portion of the ball striking face, as well as equidistantly from a heel and toe end of the ball striking face, a vertical axis comprising an axis that extends through the geometric center point, the vertical axis oriented vertically relative to a flat playing or ground surface when the club head is at an address position, a horizontal axis extending through the geometric center point, the horizontal axis perpendicular to the vertical axis and extending horizontally and generally parallel relative to the flat playing or ground surface, the horizontal axis comprising an axis that is angled at zero degrees relative to the address position when the club head is neither open nor closed at address, a hitting zone defined by an anticipated or measured area on the ball striking face where a majority of a golfer's hits typically occur, the hitting zone having generally an elliptical shape angled upwardly from a heel side of the club head to a toe side of the club head, a major axis extending through the elliptical hitting zone, the major axis defining a first principal axis of the club head, the major axis being tilted at a non-zero angle relative to the horizontal axis, a minor axis extending perpendicular to the major axis, the minor axis defining a second principal axis of the club head, the minor axis tilted at the non-zero angle relative to the vertical axis, wherein a moment of inertia of the club head about the major axis is greater than a moment of inertia of the club head about the horizontal axis, and wherein the club head further comprises a loft line extending through the geometric center point, the loft line being perpendicular to the ball striking face at the geometric center point, a center of gravity, a point of reference line extending through the center of gravity and the ball striking face, the point of reference line parallel to the loft line, and an intersection point of the point of reference line and the ball striking face, wherein the club head has a first roll radius above the intersection point, and a second roll radius below the intersection point, the first roll radius smaller than the second roll radius.

In accordance with at least another embodiment, a golf club head can comprise a ball striking face comprising a geometric center point located on a surface of the ball striking face, the geometric center point located generally equidistantly from an uppermost portion of the ball striking face and a lowermost portion of the ball striking face, as well as equidistantly from a heel and toe end of the ball striking face, a vertical axis comprising an axis that extends through the geometric center point, the vertical axis oriented vertically relative to a contact point on the bottom of the club head when the club head is at an address position, a horizontal axis extending through the geometric center point, the horizontal axis perpendicular to the vertical axis and extending horizontal with respect to the contact point, the horizontal axis comprising an axis that is angled at zero degrees relative to the address position when the club head is neither open nor closed at address, a hitting zone defined by an anticipated or measured area on the ball striking face where a majority of a golfer's hits typically occur, the hitting zone having generally an elliptical shape angled upwardly from a heel side of the club head to a toe side of the club head, a major axis extending through the elliptical hitting zone, the major axis defining a first principal axis of the club head, the major axis being tilted at a non-zero angle relative to the horizontal axis, a minor axis extending perpendicular to the major axis, the minor axis defining a second principal axis of the club head, the minor axis tilted at the non-zero angle relative to the vertical axis, wherein a moment of inertia of the club head about the major axis is greater than a moment of inertia of the club head about the horizontal axis, and wherein the club head further comprises a first roll radius above the major axis, and a second roll radius below the major axis, the first roll radius smaller than the second roll radius.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features and advantages of the present embodiments will become more apparent upon reading the following detailed description and with reference to the accompanying drawings of the embodiments, in which:

FIG. 1A is a front plan view of a golf club in accordance with at least one embodiment;

FIG. 1B is a plot diagram of a golfer's hit distribution on a hitting zone of a face of the golf club of FIG. 1A;

FIG. 1C is a side view of the golf club head of FIG. 1A;

FIG. 2 is a front plan view of a golf club in accordance with at least one embodiment;

FIG. 3 is a cross-sectional view, taken along line 3-3, of the golf club of FIG. 2; and

FIGS. 4-6 are alternative embodiments of the cross-sectional view of FIG. 3.

FIG. 7 illustrates relationships among roll radii according to various embodiments.

FIG. 8A shows an anticipated or measured area on a ball striking face where a majority of a golfer's hits may typically occur.

FIG. 8B shows an axis A and a range of locations for a plane P.

FIGS. 9A-9C illustrate a coordinate system for a club head at address and show an axis A and an axis B.

FIGS. 10A-10C show a plane P according to certain embodiments.

FIGS. 11A-11C show a distance D from a plane P according to certain embodiments.

FIGS. 12A and 12B show a weight member according to certain embodiments.

FIGS. 13A and 13B show weight members according to certain embodiments.

FIGS. 14A-14D show weight members according to certain embodiments.

FIGS. 15A-15D show a weighted area according to certain embodiments.

FIGS. 16A and 16B illustrate a system and method for identifying and measuring bulge and roll.

FIGS. 17A-17E show a club head according to certain embodiments.

FIG. 18 is a cutaway view of a club head.

FIGS. 19-26 are detail cross-sectional views of seams according to various embodiments.

DETAILED DESCRIPTION

The present application is directed to golf club heads. While the embodiments disclosed herein include club heads for wood-type clubs, it is contemplated that one or more of the concepts described herein can further be used for other types of club heads, including but not limited to hybrids, irons, and putters.

Optimized MOI

With reference to FIGS. 1A and 1B, a club head 10 can comprise a ball striking face 12. The ball striking face 12 can include, for example, a face plate 13 with score lines, or other structure(s) used to facilitate hitting a golf ball. In some embodiments, the ball striking face 12 can be comprised entirely or partially of a face insert. The club head 10 can include a vertical axis 14, and a horizontal axis 16, and a hitting zone 18. In some embodiments, the vertical axis 14 can correspond to an axis that extends through a geometric center point 20 located on the surface of the ball striking face 12. The geometric center point 20 can be a point that is generally equidistant from both a top of the ball striking face 12 (e.g. an uppermost point of the ball striking face 12 when the club head 10 is at an address position) and bottom of the ball striking face 12 (e.g. a lowermost point of the ball striking face 12 when the club head 10 is at an address position). The geometric center point 20 can be a point that is generally equidistant from a heel end of the ball striking face 12 (e.g. a point on the ball striking face 12 most distally located from the heel end of the club head 10) and toe end of the ball striking face 12 (e.g. a point on the ball striking face 12 most distally located from the toe end of the club head 10). The vertical axis 14 can extend through the geometric center point 20, and be oriented vertically relative to a flat playing or ground surface (e.g. the ground surface on a golf course) when the club head 10 is at an address position. In some embodiments, the vertical axis 14 can correspond to an axis that extends through the geometric center point 20 located on the surface of the ball striking face 12, and extends vertically along the surface of the ball striking face 12 itself, following the loft of the ball striking face 12. In other words, in some embodiments the vertical axis 14 can be defined as oriented along the ball striking face 12 itself.

With reference to FIG. 1C, in some embodiments the club head 10 can include a contact point 21. The contact point 21 can be located on the bottom of the club head 10. The contact point 21 can be a point, or area, configured to contact a flat playing or ground surface when the club head 10 is at address. The vertical axis 14 can be oriented relative to the contact point 21. For example, a vertical axis “V” can extend through the contact point 21, generally perpendicular to the flat playing or ground surface “G”, and extend through the club head 10. The vertical axis 14, which can extend through the geometric center point 20, can be parallel to the axis “V”.

The horizontal axis 16 can extend through the geometric center point 20, and can be perpendicular to the vertical axis 14. The horizontal axis 16 can extend parallel to the flat playing surface. The horizontal axis 16 can correspond to an axis that is angled at zero degrees relative to an address position that is neither open nor closed. An open address position is one in which the club head's toe is further behind the golf ball than the golf club head's heel. A closed position is one in which the club head's heel is further behind the golf ball than the golf club head's toe. An address position that is neither open nor closed is one in which the club head's heel and toe are aligned equally relative the golf ball.

Moment of inertia I (kg·m² or similar) is a measure of an object's resistance to changes to its rotation about an axis. It is the inertia of a rotating body with respect to its rotation. The moment of inertia is specified with respect to an axis of rotation. Each idealized axis through a body may have a unique moment of inertia I.

The moment of inertia of an object about a given axis describes how difficult it is to change its angular motion about that axis. Therefore, it encompasses not just how much mass the object has overall, but how far each bit of mass is from the axis. The further out the object's mass is, the more rotational inertia the object has, and the more rotational force (torque, the force multiplied by its distance from the axis of rotation) is required to change its rotation rate.

Generally, club heads are designed so that the moment of inertia about the vertical axis 14, and/or a horizontal axis 16, of the club head 10 is optimized. Thus, the club head 10 is designed with the moments of inertia about these two axes as large as possible, so that when the club head 10 is swung down and the ball striking face 12 contacts the golf ball, the club head 10 will experience as little rotational movement as possible about the vertical and horizontal axes 14, 16 as possible.

However, club heads tend to rotate about principal axes, and the principal axes are not necessarily the same as the vertical and horizontal axes 14, 16. For example, it has been found that the principal axes of a club head 10 are generally correlated to hitting zones on the club head, and that most golfers do not strike the golf ball in a hitting zone that coincides with the vertical and horizontal axes 14, 16. Rather, it has been found that most golfers generally hit the ball in an elongated hitting zone 18 that extends from a lower heel portion of the club head 10 towards an upper toe portion of the club head 10, the zone 18 having a perimeter 22. The hitting zone 18 can often take the form of an ellipse (or ellipses) angled, or tilted, up from a heel end of the club head towards a toe end of the club head. In some embodiments, the hitting zone 18 can be in the form of a series of ellipses that generally form a rhombus-like hitting pattern and zone on the club head face. Moment of inertia is discussed in U.S. Pat. No. 6,186,905; U.S. Pat. No. 6,045,455; U.S. Pat. No. 5,836,830; and U.S. Pat. No. 4,471,961, the contents of which are hereby incorporated by reference in their entirety for all purposes.

The hitting zone 18 can represent, and/or can be designed to represent, an ideal zone on the ball striking face 12 for a golfer to hit the ball. In some embodiments, the hitting zone 18 can be an area on the ball striking face 12 within which the golfer will achieve the most optimum ball flight results (e.g. distance and accuracy). For example, and with reference to FIG. 1B, the hitting zone 18 can represent an area on the club face where at least 60 percent of a golfer's shots are struck. In some embodiments, the hitting zone 18 can represent an area on the club face where at least 70 percent of a golfer's shots are struck. In some embodiments, the hitting zone 18 can represent an area on the club face where at least 80 percent of a golfer's shots are struck. In some embodiments, the hitting zone 18 can represent an area on the club face where at least 90 percent of a golfer's shots are struck.

While the hitting zone 18 is illustrated as a single ellipse in FIGS. 1A and 1B, other shapes are also possible. For example, U.S. Pat. No. 7,549,934, which is incorporated in its entirety by reference herein, describes further embodiments of a club head having a rhombus-like zone on the club head face.

Because of the tilted hitting zone 18, if the moments of inertia in the club head 10 were optimized about the vertical and horizontal axes 14, 16, the club head 10 may experience unwanted rotational movement throughout the hitting zone 18. For example, the rotational movement of the club head 10 may be significantly increased in the area of the hitting zone 18 nearest the toe end of the club 10, as this area is located further away from the vertical and horizontal axes 14, 16 than other areas of the hitting zone 18.

Therefore, it has been found advantageous to optimize the moments of inertia about the principal axes that are defined by the hitting zone 18 itself, rather than the vertical and horizontal axes 14, 16. For example, it has been found advantageous to optimize the moments of inertia about one or more of the principal axes 24 and 26 as shown in FIG. 1. Principal axes 24 and 26 can correspond to the minor and major axes of an elliptical hitting zone 18, respectively. The axes 24, 26 can be perpendicular to one another, and tilted relative to the vertical and horizontal axes 14, 16. For example, in some embodiments, the minor axis 24 can be orientated at an angle α relative to the vertical axis 14. In some embodiments, the angle α can generally be greater than about 3.0 degrees and less than about 16.0 degrees, though other ranges and values are also possible. For example, in some embodiments the angle α can be greater than about 3.0 degrees and less than about 12.0 degrees. In some embodiments the angle α can be greater than about 3.0 degrees and less than about 6.0 degrees. In some embodiments the angle α can be greater than 16.0 degrees. For example, in some embodiments the angle α can be approximately 20 degrees, or approximately 30 degrees, or approximately 45 degrees. In some embodiments the angle between the major axis 26 and the horizontal axis 16 can be equivalent to the angle α. For example, the angle between the major axis 26 and the horizontal axis 16 can be greater than about 3.0 degrees and less than about 16.0 degrees, though other ranges and values are also possible, such as those described above.

By optimizing the moments of inertia of the club head 10 about one or more of the tilted principal axes 24, 26, as opposed to the vertical and/or horizontal axes 14, 16, a moment of inertia of the club head about the minor axis 25 can be configured to be greater than a moment of inertia of the club head about the vertical axis 14. Similarly, in some embodiments a moment of inertia of the club head about the major axis 26 can be configured to be greater than a moment of inertia of the club head about the horizontal axis 16.

It can especially be beneficial to have the moment of inertia of the club head about the minor axis 25 be greater than a moment of inertia of the club head about the vertical axis 14, since most club heads tend to twist more so about the minor axis 24 than the major axis 26, due to the shape and size of the club head, and the location of weight within the club head. Overall, by optimizing the moments of inertia about one or more of the principal axes, the club head 10 can be more in tune with a golfer's typical swing and with a defined hitting zone 18. In some embodiments, so long as the golfer stays within the hitting zone 18 with his or her swing, there may advantageously be little to no unwanted rotational movement of the club head 10.

Optimized Roll

With reference to FIGS. 2-4, in some embodiments the club head 10 can be designed so that the vertical roll of the ball striking face 12 is optimized. For example, and as described above, the club head 10 can typically include a ball striking face 12 with a geometric center point 20.

With reference to FIGS. 2 and 3, the vertical roll of the club head 10 can be defined as the value of a radius R at any given point along the ball striking face 12, as measured from a side view of the club head 10 like that in FIG. 3. The radius R can be a measurement, for example, of how the ball striking face 12 is curving. For example, the radius R can be measured generally about a series of horizontal axes 28, as shown in FIG. 2, the radius R indicating how the ball striking face 12 is curving along a vertical direction from a crown to sole of club head 10 about each of the horizontal axes 28. Thus, roll radius can be defined, for example, as it is defined in Werner and Greig, ‘Optimum Face Curvature for Golf Clubs’, Chapter 18 of How GOLF CLUBS REALLY WORK, 2000, Origin, Inc., Jackson W Y, pp. 81-83. In an alternative embodiment, face curvature is defined with reference to a loft line normal to and passing through a geometric center of the strike face, a reference line through a club head center of gravity and parallel to the loft line, a measuring line on a surface of the strike face comprising a series of evenly spaced points, and N surface normals, each normal to and extending from the strike face at one of the points and each defining an angle θ_(N) with the next, discussed below with reference to FIGS. 16A and 16B.

In some club heads 10, and with reference to FIG. 3, the center point 20 can represent an outward peak along the ball striking face 12 when the club is viewed from the side, and the roll radius R can remain constant both above and below the geometric center point 20. Because of the constant vertical roll radius R, the loft of the club head 10 decreases below the geometric center point 20 in these clubs, and increases above the geometric center point 20. Therefore, if a golf ball is struck below the geometric center point 20, the ball will typically see less loft than if it was struck at the geometric center point 20, or above the geometric center point 20, and will therefore launch with lower trajectory.

With reference to FIG. 4, in at least one embodiment the geometry of a ball striking face 12′ can be altered such that the ball striking face 12′ has a first roll radius R1 above the geometric center point 20′, and a second roll radius R2 below the geometric center point 20′ (i.e., such that a θ_(i) above the reference line is larger than a θ_(j) beneath the reference line according to the measuring system defined with reference to FIGS. 16A and 16B). R2 can be greater than R1. By decreasing the roll radius R1 above the geometric center point 20′, the top of the ball striking face 12′ can take on more of a rounded shape when viewed from a side of the club head 12′. In some embodiments this rounded shape can provide additional loft to a golf ball, as compared for example with the club shown in FIG. 3, depending on the magnitude of radius R1. In some embodiments, the increased roll radius R2 below the geometric center point 20′ can provide additional loft to the golf ball as well, as compared with the club shown in FIG. 3. The increased roll radius R2 below the geometric center point 20′ can give a lower portion of the ball striking face 12′ more of a flattened, or trough-like appearance. In some embodiments the increased roll radius R2 can approximate the roll radius at the geometric center point 20′, and can thus make a hit below the geometric center point 20′ still have approximately the same carrying distance as a hit at the geometric center point 20′. In some embodiments the roll radius R1 can generally be held constant along a top portion of the face, and the roll radius R2 can generally be held constant along a bottom portion of the face. In some embodiments the roll radius R1 and/or R2 can vary and transition along the top portion of the face and/or bottom portion of the face. In some embodiments, the roll radius R1 and/or R2 can be different for each different loft angle of a club head. For example, depending on the type of loft one selects for a particular club head, the roll radius R1 and/or R2 can be optimized differently. In some embodiments, a golfer can optimize the club head speed and ball striking distance for each club head by tailoring the roll radii R1, R2. Roll radii are discussed in U.S. Pat. No. 6,595,869; U.S. Pat. No. 6,558,272; U.S. Pat. No. 6,454,664; U.S. Pat. No. 6,428,426 and U.S. Pub. 2011/0151994, the contents of which are hereby incorporated by reference in their entirety for all purposes.

With continued reference to FIG. 4, in some embodiments a roll radius can be calculated by using at least three points on the ball striking face 12′. For example, points 20′, 20 a′, and 20 b′, can be identified on the club head. Points 20 a′ and 20 b′ can be located equidistantly away from point 20′. An equivalent radius arc Req can be formed through the three points, or a locus of points, the arc having a radius that approximates the exact roll radius at 20′.

In some embodiments, if a golfer “mishits” a golf ball far above the geometric center point 20′, the reduced roll radius R1 above the geometric center point 20′ can facilitate a higher trajectory for the flight of the ball, resulting in a longer ball flight length. Similarly, if a golfer “mishits” a golf ball far below the geometric center point 20′, the increased roll radius R2 can facilitate a higher trajectory for the flight of the ball, resulting in a longer ball flight path. Thus, by having a golf club head with a decreased roll radius R1 above geometric center point 20′, and an increased roll radius R2 below geometric center point 20′, even if the golfer “mishits” the ball, the ball flight path can still be optimized.

While the geometric center point 20′ as defined above can be an optimized location for hitting the ball and getting the longest ball flight path, in some embodiments the geometric center point 20′ may not be the optimized location for hitting a golf ball. For example, the center of gravity and/or club speed may be such that the optimized location for hitting a golf ball falls below the typical geometric center point 20′. Thus, in some embodiments the transition between R1 and R2 can be configured to occur at a location or locations on the ball striking face away from the geometric center point 20′, and/or away from a particular axis 28 containing the geometric center point 20′.

In some embodiments the roll radius R can preferably be approximately 250 mm at the axis 28 that contains the geometric center point 20′, and can range from approximately 250 mm to 800 mm below the axis 28 that contains the geometric center point 20′, and can range from approximately 250 mm to 200 mm above the axis 28 that contains the geometric center point 20′. In some embodiments, the roll radius can preferably range from approximately 250 mm to 600 mm below the axis 28 that contains the geometric center point 20′. In some embodiments, the roll radius can preferably range from approximately 250 mm to 400 mm below the axis 28 that contains the geometric center point 20′. In some embodiments, the roll radius can remain generally constant above the axis 28 that contains the geometric center point 20′, for example at approximately 250 mm.

In some embodiments, the roll radius can be optimized about axes other than the horizontal axes 28. For example, and with reference to FIG. 2, in some embodiments the roll radius can be optimized about axes 30. For example, the roll radius can be optimized about axes that are in line with and are parallel to a major axis of a typical hitting pattern on a club head, such as axis 26 described above and illustrated in FIG. 1. Because the club head 10 typically may want to twist and/or rotate about principal axes, as opposed to a vertical and/or horizontal axis as described above, it can be advantageous to incorporate a roll radius that is aligned with the principal axis. This can especially be true if the anticipated or measured hitting pattern is the optimized location for hitting the ball and obtaining the longest ball flight path.

If the axis 30 that contains the geometric center point 20′ generally represents an optimized location for hitting the golf ball, then it can be advantageous to have a decreased roll radius above the axis 30 that contains the geometric center point 20′, and an increased roll radius below the axis 30 that contains the geometric center point 20′. This alignment of roll radii can make the club head 10 more consistent in terms of how far the ball will be hit depending on a given hitting pattern, and the club's general inclination to twist and/or move about the principal axes.

In this manner, if the golfer “mishits” the golf ball above a particular axis 30, the trajectory will be increased accordingly to account for the mishit, and similarly if the golfer “mishits” the golf ball below a particular axis 30, the trajectory will also be increased accordingly to account for the mishit.

In some embodiments the roll radius can preferably be approximately 250 mm along a tilted axis 30 that contains the geometric center point 20′, and can range from approximately 250 mm to 800 mm below the axis 30 that contains the geometric center point 20′, and range from approximately 250 mm to 200 mm above the axis 30 that contains the geometric center point 20′. In some embodiments, the roll radius can preferably range from approximately 250 mm to 600 mm below the axis 30 that contains the geometric center point 20′. In some embodiments, the roll radius can preferably range from approximately 250 mm to 400 mm below the axis 30 that contains the geometric center point 20′. In some embodiments, the roll radius can remain generally constant above the axis 30 that contains the geometric center point 20′, for example at approximately 250 mm.

With reference to FIG. 5, in some embodiments, the club head 10 can include a ball striking face 12″ with a point of reference line 32 that extends through a center of gravity location 34 of the club head 10. The point of reference line 32 can be defined, for example, with a mathematical equation, such as a higher order polynomial equation. The point of reference line 32 can be parallel to a loft line 36 that extends through the geometric center point 20″ of a ball striking face 12″, the loft line 36 being perpendicular to the ball striking face at the geometric center point 20″.

In some embodiments an intersection point 38 of the point of reference line 32 and the ball striking face 12″ can comprise an ideal location for a golfer to hit the ball. The intersection point 38 can comprise an ideal location for the transition of a roll radius as well. For example, the intersection point 38 can be located along a horizontal, or tilted axis on the ball striking face 12″, such that the roll radius above the axis is lower than the roll radius below the axis, similar to what is shown in FIG. 4 with radii R1 and R2. In some embodiments, the intersection point 38 can comprise a point along an axis that forms a major axis of an anticipated or measured hitting zone, such as an axis 30 as described above.

With continued reference to FIG. 5, in some embodiments the surface along the ball striking face 12″ can be optimized for various swing characteristics by expressing surface normals (i.e. axes that extend perpendicular to the ball striking face 12″, such as loft line 36), as a percentage of a defining loft of the club. For example, in some embodiments the surface normals of a ball striking face 12″ can be closely tied to a manufactured loft of the club below the intersection point 38, and can diverge quickly away from the manufactured loft above the intersection point 38, thereby giving the ball striking face 12″ a sharply rounded shape on top when viewed from the side, and a more gradually sloping shape along the bottom.

In some embodiments the roll radius can preferably be approximately 250 mm along an axis containing the intersection point 38, and can range from approximately 250 mm to 800 mm below an axis containing the intersection point 38, and range from approximately 250 mm to 200 mm above the an axis containing the intersection point 38. In some embodiments, the roll radius can preferably range from approximately 250 mm to 600 mm below an axis containing the intersection point 38. In some embodiments, the roll radius can preferably range from approximately 250 mm to 400 mm below an axis containing the intersection point 38. In some embodiments, the roll radius can remain generally constant above an axis containing the intersection point 38, for example at approximately 250 mm.

With reference to FIG. 6, in some embodiments, the club head 10 can include one, two, or more roll radii or bulge radii. While discussed herein in terms of roll, it will be appreciated that the concepts and embodiments are applicable to bulge, which may generally be considered to be a curvature of a face around an axis orthogonal to an axis of curvature for a roll radius. That is, roll is curvature along a crown-to-sole direction, while bulge is curvature along a heel-to-toe direction.

In FIG. 6, arrow X_(F) indicates a one-dimensional measurement of distance along a surface of a club starting at an arbitrary point on the crown and extending over a face towards the sole. At any given point in the X_(F) direction, a face may have a roll radius Rn. A club head of the present invention may include any number of different roll radii (e.g., one, two, zero (all flat), three, etc.). Club head 40 in FIG. 6 is shown to include at least two different roll radii, R1 and R₂. Club head 40 may further include a third roll radius R_(n). For convenience's sake, a flat zone of the face is defined as having a roll radius R_(n) of some arbitrarily high measurement. For example, a portion of a face with a roll radius of 1 Km may be indistinguishable from a portion of a face that is flat for all practical purposes in the golf club arts. Thus a flat area of a club head can be defined as having a roll radius of 10⁶ mm or any reference to a roll radius of some arbitrarily high number such as 10⁶ mm can be taken to refer to a flat zone.

The ray lines shown in FIG. 6 are used to distinguish some exemplary points on the face based on roll radius. As the distance between the ray lines is diminished, a graph of R over X_(F) will begin to take on a line-like appearance.

FIG. 7 illustrates relationships among roll radii according to various embodiments. As shown in FIG. 7, embodiments of the invention include a roll radius RL near a crown and a higher roll radius R2 near a sole. In some embodiments, RL and R2 may be separated by one or more other roll radii including Rn, which can be a third, intermediate roll radius or an arbitrarily high roll radius (e.g., flat zone of a club face).

Face curvature can further be defined with reference to a system illustrated in FIG. 16A.

FIG. 16A illustrates a system for defining face curvature. FIG. 16A shows a cross-sectional view through a face of a club head along a measuring line on a surface of the strike face. The measuring line includes a series of evenly spaced points and N surface normals, each normal to and extending from the strike face at one of the points and each defining an angle θ_(N) with the next. In some embodiments, face curvature is further defined with reference back to FIG. 5. FIG. 5 shows a loft line normal to, and passing through a geometric center of, the strike face and a reference line through a club head center of gravity and parallel to the loft line. Making reference to the defining systems of FIGS. 5 and 16A, FIG. 16A illustrates a club head in which a θ_(i) above the reference line is larger than a θ_(j) beneath the reference line, such that a crown portion of the strike face is more curved than a sole portion of the strike face.

The surface normals illustrated by FIG. 16A can further be described by a plot of angle θ_(N) over spacing XF along the measuring line. As the distance between the ray lines is diminished, a graph of R over X_(F) will begin to take on a line-like appearance.

FIG. 16B illustrates face curvatures according to various embodiments. As shown in FIG. 16B, embodiments of the invention include one 0, near a crown and a lower θ_(j) near a sole. In some embodiments, θ_(i) and θ_(j) may be separated by one or more other θ_(N) such as θ_(k) that is zero (e.g., flat zone of a club face) or that is between θ_(i) and θ_(j). The traces shown in FIG. 16B are discussed in more detail below.

In some embodiments, a club head includes at least two roll radii or face curvatures. In certain embodiments, a curved area near a crown and a curved area near a sole are separated by a flat zone (i.e., having roll radii Rn being arbitrarily high or a θ_(N) of zero). In some embodiments, the separation between areas having different curvatures extends horizontally across a club face when a club is at address. In certain embodiments, the separation between curvatures is non-horizontal (e.g., 5°, 10°, 20°, or more from the horizontal). In certain embodiments, the separation is parallel to an axis of a hit pattern.

FIG. 8A shows a hit pattern according to certain embodiments. When the hit pattern shown in FIG. 8A is approximated by an ellipse. reference can be made to a major and minor axis of the ellipse. Accordingly, reference can be made to a major and minor axis of a hit pattern. FIG. 8B shows an axis A, which can represent a minor axis of a hit pattern, and a range of locations for a plane P. In some embodiments, plane P includes a major axis of a hit pattern. In certain embodiments, plane P includes an intersection of a major and minor axis of a hit pattern and a line that is within a certain some number of degrees of rotation from the major axis. As shown in FIG. 8B, plane P can be between lines 51 and 52 (e.g., right on line 55). The location of lines 51 and 52 in FIG. 8B is arbitrary and they can be spaced apart farther than is shown in FIG. 8B (e.g., to define an angle of 5°, 15°, 30°, 60°, or more with each other in the plane of the page).

FIGS. 9A-9C illustrate a coordinate system for a club head at address and show an axis A and an axis B. As shown in FIGS. 9A-9C, when a club head is at address. the x direction extends generally face-to-aft; the y direction extends generally heel-to-toe; and the z direction extends generally vertical. FIG. 9B is drawn to include axes A and B and their locations in the Y and Z directions within club head 50. In the X direction, either or both of axes A and B can be in any place in various embodiments. In certain embodiments, either or both of axes A and B are tangent to a geometric center of a strike face. In certain embodiments, either or both of axes A and B pass through an average or intended center of percussion of hits. Center of percussion is discussed in U.S. Pat. No. 5,803,830; U.S. Pat. No. 5,629,475; and U.S. Pat. No. 4,674,746, the contents of which are hereby incorporated by reference in their entirety for all purposes. In certain embodiments, either or both of axes A and B pass through a center of gravity of a club head. The intersection between A and Z as shown in FIG. 9C is shown in an arbitrary location and it may be anywhere (e.g., at or near a center of percussion, on or near a spot on the strike face, at or near a center of gravity) according to various embodiments.

Axis A may define an idealized plane P normal to axis A. FIGS. 10A-10C show plane 55 as plane P intersecting club head 50 according to certain embodiments.

Making reference to FIG. 9B and FIGS. 10A-10C, it will be appreciated that the intersection of plane P and a club head will vary in location as angle θ_(A) and θ_(C) vary. In some embodiments, θ_(C) is less than about 5° (e.g., zero), although it may be about 15° or more. For any given angle θ_(A) and θ_(C), plane P will intersect club head 50 to define a club head intersection, as illustrated in FIGS. 10A-10C. In certain embodiments, axis A is normal to plane P and axis A passes through or near club head 50 (e.g., at or near a center of percussion, on or near a spot on the strike face, at or near a center of gravity). In certain embodiments, θ_(C) is determined so that plane P passes through and intersects an aft-most point on a club head, or at least within a few centimeters of an aft-most point (e.g., within 1 cm of an aft-most point). In some embodiments, P passes through, or within less than a few cm (e.g., <1 cm) of a geometric center of a strike face, a center of percussion, an aft-most point of a club head, or any combination thereof.

Club head 50 includes a moment of inertia around axis A. In some embodiments, a moment of inertia around an axis A is higher than a moment of inertia around an axis Z. In some embodiments, club head 50 includes a weighted area within a certain distance D of plane P, wherein A is normal to P (i.e., to contribute to a moment of inertia around axis A).

FIGS. 10A-10C show a plane P intersecting club head 50. As shown in FIGS. 10A, the plane P intersects the strike face of club head 50. FIG. 10B shows plane P intersecting a heel side of a sole of club head 50. FIG. 10C shows plane P intersecting a toe side of a crown of club head 50. To optimize a MOI about an axis normal to plane P, mass is concentrated in, or close to, plane P on club head 50. Preferably, mass is concentrated within a distance D of plane P. The distance D can be varied to achieve design goals. For example, it can be about 3 cm or less (e.g., about 2 cm or 1 cm).

FIGS. 11A-11C show a distance D from a plane P according to certain embodiments. As shown in FIGS. 11A-11C, the distance D defines an idealized upper plane P′ and an idealized lower plane P″.

FIGS. 12A-15D each show an example of a club head having a body wall in which a weighted area of the body wall has a mass per unit area greater than an overall mass per unit area of the body wall. In each of those figures, the weighted area is within a distance D of about 3 cm from a plane P that intersects the strike face, a toe side of a crown of the body, and a heel side of a sole of the body. Any suitable method may be used to provide a club head having a moment of inertia as described herein. MOI is discussed in U.S. Pat. No. 8,025,581 and U.S. Pub. 2009/0191980, the contents of which are hereby incorporated by reference in their entirety for all purposes. In certain embodiments, a club is provided that has one more weight members disposed therein between upper plane P′ and lower plane P″.

FIGS. 12A and 12B show a club head 60 having a weight member 62 that generally has a ridge-like structure and is disposed near a club head intersection of plane P with club head 60. As can be seen in FIGS. 12A and 12B, weight member 62 is closer to the crown than to the sole on a toe side of the club, and closer to the sole than to the crown on a heel side of the club head. Weight member 61 can include any suitable material such as, for example, a metal weld, a polymer, a urethane-based material, a silicone-based material, a composite, a putty-like material, or similar and may be impregnated with, or have embedded therein, high density material such as tungsten or lead.

Weight member 62 may form one continuous closed loop all around club head 60, or have an open “C” shape (as shown). Weight member 62 may be entirely within a distance D of plane P, or only partially with distance D (i.e., 70% or 80%, for example, of weight member 62 may be within distance D of plane P). Weight member 62 imbues club head 60 with an optimized MOI around axis A. In some embodiments, D is about 3 cm or about 2 cm.

FIGS. 13A and 13B show club head 70 including toe-crown weight members 72 and heel-sole weight members 74 according to certain embodiments. As shown in FIGS. 13A and 13B, club head 70 has four weight members affixed therein within a distance D of plane P. In some embodiments, club head 70 has one weight member, or two, or three, or five, or six, or more, affixed therein. The weight members may generally be provided as pads, e.g., of metal, fixed therein, e.g., welded or cemented.

FIGS. 14A-14D show a club head 80 including weight members 87 positioned in recesses 85 according to certain embodiments. Recesses 85 can be provided that are open towards an outside of the club head. A club head can be provided with weight members 87 that fit into recesses 85. In some embodiments, a golfer or a pro-shop consultant can choose from among a set of weight member 87 and then fix the weight members into the recesses (e.g., with cement, a press-fit, or a spot weld). The weight members are thus affixed to the club head within a distance D of plane P that is orthogonal to an axis A that forms a non-zero angle θ_(A) with a vertical axis Z when the club head is at addresses. In some embodiments, D is about 4 cm. In certain embodiments, D is less than 3 cm (e.g., less than about 2 cm). In certain embodiments, the weight members are affixed to the club head essentially where the plane intersects the club head (e.g., D<1 cm).

FIGS. 15A-15D show a club head 90 wherein construction seams provide a weighted area according to certain embodiments. As shown in FIGS. 15A-15D, a crown may be joined to a sole via an intermediary piece (e.g., a skirt member). In some embodiments, a crown portion meets a sole portion directly. Two portions of a club head that meet may be affixed together to define a seam that creates a local increase in mass distribution. In certain embodiments, a seam includes a portion of overlap of two adjacent portions. In some embodiments, each portion has a flange that can include a turned-in edge of the portion such that the two portions meet at, and can be joined via, the flanges (e.g., by welding or cementing). Assembly seams are discussed in U.S. Pub. 2012/0172147; U.S. Pat. No. 8,147,354; U.S. Pub. 2010/0041494; and U.S. Pub. 2005/0059508, the contents of which are hereby incorporated by reference in their entirety for all purposes.

FIG. 15D illustrates the use of seams wherein a crown member meets a skirt member that also meets a sole member, each seam involving two flanges such that the club includes, as a weighted area, four joined flanges around the club head within a distance D of plane P. It will be appreciated by comparing, for example, FIG. 15B to FIG. 13B that construction seams may be purposefully located near plane P. FIG. 13B shows a club head in which a crown-skirt and skirt-sole construction seam are located arbitrarily on a heel side of a club. FIG. 15B shows a club head in which a crown-skirt and skirt-sole construction seam are located to take advantage of mass that can be associated with a construction seam to optimize an MOI of a club head. Further, a construction seam can be associated with additional mass than is required for construction. For example, a heavy adhesive can be used (e.g., cement impregnated with a metal). Further, a club head such as the one shown in FIGS. 15A-15D could have any of the seam constructions illustrated in FIGS. 18-26. In some embodiments, weight members are joined to the club head at a construction seam (e.g., held in place with the assistance of one or more flanges as can be seen in heel-side seam 95 or toe-side seam 97 in FIG. 15D). In certain embodiments, heel-side seem 95 and toe-side seam 97 together define a u-shaped groove within club head 90 that can provide a weighted area. Seam attachment and weight is discussed in U.S. Pub. 2011/0053706, the contents of which is hereby incorporated by reference in its entirety for all purposes.

Two components can be attached at a seam by any suitable method and mechanism including, for example, welds, adhesives, mechanical fasteners, or others. In certain embodiments, an adhesive such as an epoxy is used. One suitable adhesive is HYSOL 193052 epoxy. Further, as assembly seam can be formed via co-molding. Co-molding is discussed in U.S. Pub. U.S. Pub. 2011/0053706.

By locating heel-side seam 95 or toe-side seam 97 within a distance D of plane P, a moment of inertia may be thus optimized about a normal to plane P. Where plane P is located to intersect or pass close to a major axis of a hit pattern, a club is thus provided that naturally resists twisting during off-center hits.

Further, where hits may be off-center in a crown-sole direction (i.e., a frequency of hits exhibits an approximately normal distribution over a minor axis of a hit pattern), a moment of inertia may further be optimized about an axis that is substantially perpendicular to the minor axis of the hit pattern. Thus, a weighted area may be provided in a club head near a crown or a sole in a pattern that tends to increase a moment of inertia I_(B) around an axis B that forms a non-zero angle θ_(B) with a horizontal plane when a club head is at address. Moment of inertia I_(B) may be optimized by any suitable mass distribution design, such as any of those described herein.

Further, a club head of the present invention may optionally include none, one, two, three, or more roll radii. For example, club head 90 shown in FIGS. 15A-15D includes strike face 93. Strike face 93 can include two roll radii. In certain embodiments, a strike face has an area with a first roll radii near the crown and an area with a larger roll radii near the sole. The two areas may be separated by a line or by a flat area. In certain embodiments of the present invention, the separation between areas of distinct roll radii lies parallel to, or near parallel to, plane P. For example, strike face 93 as shown in FIG. 15A may include a first and a second roll radius that are separated by an idealized line that extends across the strike face from toe-side seam 97 to heel-side seam 95.

FIGS. 16A and 16B illustrate a system and method for identifying and measuring bulge, roll, or both. With reference here to roll, to illustrate, FIG. 16A illustrates a dimension X_(F) for making a distance measurement.

A line X_(F) starts an arbitrary point on a crown of a club head and extends across a strike face towards a sole. A series of surface normal 42 a, 42 b, . . . , 42 n are distributed equidistantly along X_(F). A distance ΔX_(F) separates each pair of adjacent surface normals. Each surface normal 42 _(i) defines an angle θ_(Ni) with adjacent surface normal 42 _(i+1). The angles θ_(Nn) can be plotted along an axis X_(F) such that each θ_(Ni) spans ΔX_(F) of axis X_(F). For ΔX_(F) greater than zero, the plot will appear as a step function (e.g., corresponding to second trace 44, third trace 45, fourth trace 46, or fifth trace 47 in FIG. 16B. As ΔX_(F) approaches zero, the plot will take on the appearance of a continuous function, as may be illustrated by trace 43 in FIG. 16B.

FIG. 16B shows a plot of angles between adjacent surface normal along a line across a strike face over which the surface normal are evenly spaced. FIG. 16B is presented without units, and any suitable scale may be applied. In certain embodiments, the invention provides a golf club having a trace that—when plotted according to angles between consecutive pairs of evenly spaced surface normals—has two portions at different heights (e.g., trace 45 or trace 43). In some embodiments, a club head has a trace with three portions, a middle one of which is substantially zero (e.g., trace 47). In some embodiments, a club head has a trace with a series of steps from one portion to another (e.g., trace 46). In certain embodiments, a club head has a trace defining a series of steps with a low central portion (e.g., trace 44).

In some embodiments a golf club head can be configured to have its moment of inertia optimized about at least one principal axis based upon an anticipated or measured hitting zone, as well as have its roll radius along the ball striking face optimized such that the roll radius is decreased above the at least one principal axis, and increased below the at least one principal axis.

In some embodiments a golf club head can be configured to have its moment of inertia optimized about at least one principal axis based on an anticipated or measured hitting zone, as well have its roll radius along the ball striking face optimized such that the roll radius is decreased above an axis containing a geometric center point, and increased below the axis containing the geometric center point.

In some embodiments, a golf club head can be configured to have an optimized moment of inertia about at least one principal axis based on an anticipated or measured hit pattern, as well as have its roll radius along the ball striking face optimized so that the roll radius is decreased above an axis containing an intersection point corresponding to a center of gravity, and increased below the axis containing the intersection point.

In some embodiments, a club can be tuned according to a specific player. For example, in some embodiments a specialized set of roll radii can be generated along the club head face, dependent on particular player characteristics including but not limited to swing speed, height, length of club shat, etc. In some embodiments, a specialized set of roll radii can be generated for each different club in a given club set. For example, a set of clubs can include clubs of different lofts, with different roll radii on each club face, depending on the desired loft. In some embodiments, the desired lofts can be tuned to the particular player. Thus, the optimized moment of inertia and optimized roll concepts described above can be specially tuned to accommodate particular player needs.

As discussed above with reference to FIGS. 15A-15D, assembly seams joining two or more components can be manipulated to tune mass properties such as moment of inertia and center of gravity. Using this concept of the invention, a designer can locate a maximum or local maximum MOI around any desired axis.

For example, FIGS. 17A-17E show a club head 101 in which a crown component 103 is jointed to a sole component 105 at assembly seam 113. Club head 101 can be, for example, a driver head with strike face 109 and hosel 107 ready to be assembled to a shaft for playing. Assembly seam 113 represents a local concentration of mass (relative to other areas of crown component 103, sole component 105, or both). Since assembly seam 113 is a local concentration of mass, and since assembly seam 113 substantially occupies a single plane, club head 101 includes a local maximal MOI around an axis normal to that plane.

As shown in FIGS. 17A-17E, assembly seam 113 is relatively low on the club head when at address (e.g., as considered to club head 50 as depicted in FIG. 10C). Further, in the depicted embodiment, assembly seam 113 is substantially in a horizontal plane when the club head is at address. In alternative embodiments, assembly seam 113 is substantially in a plane that is tilted relative to the horizontal when a club head is at address, as discussed throughout above.

Since assembly seam 113 is low on club head 101 and in a horizontal plane, club head 101 has a high MOI around a vertical axis and a low CG. This can be accomplished by simply fastening crown component 103 to sole component 105 via a method that adds a local concentration of mass. In a preferred embodiment, assembly seam 113 includes a mass-building feature not required for assembly but included for additional mass.

For example, FIG. 18 gives a cutaway view of club head 101 in which it can be seen that crown component 103 and sole component 105 are joined at inward-directed flanges and further that the flange of crown component 103 has excess material that is bent down over the flange of sole component 105. Any assembly seam with an additional mass feature and any method of assembling club head components that adds additional mass is within the scope of the invention.

FIGS. 19-26 are detail cross-sectional views of seams according to various embodiments and corresponding to the circled area of FIG. 18. Each of these embodiments can also provide a seam for a club head such as the one depicted in FIGS. 15A-15C.

In FIG. 19, a filler 119 is sandwiched between the flanges of crown 103 and sole 105. Filler 119 can include any suitable material. Preferably, filler 119 includes a heavy material, such as a metal like lead, tungsten, or iron, a rubber, or a thermoplastic material. In some embodiments, filler member 119 is the same material or a similar material to crown 103, sole 105, or both, and adds significant additional mass by virtue of the fact that it protrudes into an interior volume of the club head. In certain embodiments, filler 119 is a urethane, urethane polymer, or other polymer such as polyvinyl chloride. Filler 119 can include silicone, or can be a composite of different materials.

FIG. 20 shows an embodiment in which seam 113 is folded back on itself to create a four ply region 121 of material that is “4 ply”, i.e., a section through the flanges will traverse four thickness of flange material. Note also that a seam 113 can include a 3-ply region 120. The flanges can be folded on themselves multiple times to make, for example, a 5-play, 6-ply, 7-ply, 8-ply, etc., flange. Multi-ply region 121 generally constitutes part of seam 113 around a circumference of club head 101.

FIG. 21 shows an alternative folding pattern producing two ply region 121.

FIG. 22 illustrates an embodiment in which a filler 119 is fixed between the flanges and not visible from an exterior of the club head.

FIG. 23 shows an embodiment in which at least one flange is curled back to form an enclosure. Both flanges can be joined and curled to form an enclosure with a two ply cover. In some embodiments, each flange independently curls back on itself so that seam 113 includes two adjacent enclosures. The enclosure can be empty, partially filled, or completely filled (e.g., with filler 119).

FIG. 24 shows an embodiment in which two flanges are fastened together with a mechanism such as a rivet, screw, bolt, or similar. Fastening member 121 may pass through both flanges. Fastening member 121 may itself add substantial weight, weight bar 127 may additionally be included, or both. Two flanges can be attached together by heat staking.

Heat staking is a means of locking club head components together. In general, one of the parts to be assembled is designed to include a plastic post or tab which can be inserted through a hole or aperture in another part and then permanently and inelastically deformed by the generation or application of heat by some tool surface which effects plastic deformation. This use of the staking device results in the deformation of the heated leading end of the heat-stake such that a “mushroom cap” may be formed. The mushroom cap of each heat stake commonly covers the corresponding receiving hole of the encapsulate. This resulting overlap results in the mechanical coupling of the first and second components. The resulting retention force of a heat staking process may be tuned by varying the amount of surface area of the encapsulate contacted by the heat-stake's mushroom cap as well as the composition states of the encapsulate and heat-stake.

A particular advantage of heat stake in club head assembly is that such methods operate well with dissimilar materials. For example, a plastic component with stakes can be fastened to a metal component with receiving holes by heat staking. Heat staking is discussed in more detail in U.S. Pat. No. 6,840,755; U.S. Pat. No. 6,296,470; U.S. Pat. No. 5,871,784; U.S. Pat. No. 4,767,298; and U.S. Pub. 2008/0230948, the contents of each of which are hereby incorporated by reference in their entirety for all purposes.

FIG. 25 shows a seam 113 with a spacer panel 123 between crown panel 103 and sole panel 105. Even with simple construction as shown, this embodiment can add substantial mass due to the fact that the seam mass is effectively doubled. Further, each individual seam may be fashioned to heighten the mass concentration (e.g., by any of the embodiments shown herein).

FIG. 26 illustrates an embodiment in which a spacer panel 123 is included and a gap within seam 113 is filled with filler 119. As shown for example here, seam 113 can include any combination of methods and mechanisms to heighten a mass concentration.

While some of the embodiments described above have been described generally in the context of a driver or wood-type club, these concepts can also be included in other types of clubs, including but not limited to a hybrid, driver, or putter.

Additionally, although these inventions have been disclosed in the context of certain preferred embodiments and examples, it will be understood by those skilled in the art that the present inventions extend beyond the specifically disclosed embodiments to other alternative embodiments and/or uses of the inventions and obvious modifications and equivalents thereof. In addition, while several variations of the inventions have been shown and described in detail, other modifications, which are within the scope of these inventions, will be readily apparent to those of skill in the art based upon this disclosure. It is also contemplated that various combinations or sub-combinations of the specific features and aspects of the embodiments can be made and still fall within the scope of the inventions. It should be understood that various features and aspects of the disclosed embodiments can be combined with or substituted for one another in order to form varying modes of the disclosed inventions. Thus, it is intended that the scope of at least some of the present inventions herein disclosed should not be limited by the particular disclosed embodiments described above. 

1. A golf club head comprising: a hosel, strike face, and a body wall defining a hollow body substantially enclosing an inner volume; and a weighted area of the body wall having a mass per unit area greater than an overall mass per unit area of the body wall, the weighted area being within a distance D of about 3 cm from a plane P that intersects the strike face, a toe side of a crown of the body, and a heel side of a sole of the body.
 2. The club head of claim 1, wherein a crown portion of the strike face is more curved than a sole portion of the strike face, as defined by: a loft line normal to, and passing through a geometric center of, the strike face; a reference line through a club head center of gravity and parallel to the loft line; a measuring line on a surface of the strike face comprising a series of evenly spaced points; and N surface normals, each normal to and extending from the strike face at one of the points and each defining an angle θ_(N) with the next such that a θ_(i) above the reference line is larger than a θ_(j) beneath the reference line.
 3. The club head of claim 2, wherein the measuring line intersects the reference line and a vertical plane.
 4. The golf club of claim 1, wherein the plane P intersects a horizontal plane to define an angle between about 20° and about 40° when the club is at address.
 5. The club head of claim 4, wherein the plain P intersects the strike face within about 2 cm of a center of percussion.
 6. The club head of claim 5, wherein the plane P intersects the body within about 2 cm of an aft-most point on the club head.
 7. The club head of claim 5, wherein D is about 1 cm.
 8. The club head of claim 4, wherein the weighted portion of the body comprises two or more weight members fixed to the hollow body.
 9. The club head of claim 4, wherein the weighted portion of the body comprises a joining seam between a crown component and a sole component of the body wall.
 10. The golf club head of claim 9, wherein the seam comprises a filler material.
 11. The club head of claim 10, wherein a portion of seam is N-ply, and N>2.
 12. A golf club head comprising: a body coupled to a hosel; a moment of inertia I_(Z) about an axis Z, wherein Z is vertical when at address; a moment of inertia I_(A) about an axis A, wherein A intersects Z to define a non-zero angle θ_(A), and further wherein I_(A) is greater than I_(Z); and a strike face with a striking surface, wherein points evenly spaced in a line on the surface define N surface normals, each defining an angle θ_(N) with the next, such that a θ_(i) near a crown of the club head is larger than a θ_(j) near the sole.
 13. The golf club head of claim 12, wherein the angle θ_(A) is between about 5° and about 45°.
 14. The golf club head of claim 12, further comprising: a crown panel; a sole panel; and an assembly seam between the crown panel and the sole panel, the seam extending at least about halfway around the club head, wherein the assembly seam lies within a distance D of a plane P that is perpendicular to axis A, and D is less than about 2 cm.
 15. The golf club head of claim 14, wherein the seam comprises a filler material.
 16. The club head of claim 14, wherein a portion of seam is N-ply, and N>2.
 17. The golf club of claim 14, wherein θ_(A) is greater than 20° and θ_(B) is greater than 20°.
 18. The golf club head of claim 12, further comprising: a moment of inertia I_(Y) about an axis Y, wherein Y is horizontal and extends through a heel side of the club head and a toe side of the club head when the club is at address; and a moment of inertia I_(B) about an axis B, wherein B intersects Y to define a non-zero angle θ_(B), and further wherein I_(B) is greater than T_(Y).
 19. The golf club of claim 14, wherein θ_(B) is between about 5° and about 45°.
 20. The golf club head of claim 12, wherein the line is vertical and there is a θ_(k), such that i≦k≦j and θ_(k)=0.
 21. A golf club head comprising: a ball striking face comprising: a geometric center point located on a surface of the ball striking face, the geometric center point located generally equidistantly from an uppermost portion of the ball striking face and a lowermost portion of the ball striking face, as well as equidistantly from a heel and toe end of the ball striking face; a vertical axis comprising an axis that extends through the geometric center point, the vertical axis oriented vertically relative to a flat playing surface when the club head is at an address position; a horizontal axis extending through the geometric center point, the horizontal axis perpendicular to the vertical axis and extending horizontally and generally parallel to the flat playing surface, the horizontal axis comprising an axis that is angled at zero degrees relative to the address position when the club head is neither open nor closed at address; a hitting zone defined by an anticipated or measured area on the ball striking face where a majority of a golfer's hits typically occur, the hitting zone having generally an elliptical shape angled upwardly from a heel side of the club head to a toe side of the club head; a major axis extending through the elliptical hitting zone, the major axis defining a first principal axis of the club head, the major axis being tilted at a non-zero angle relative to the horizontal axis; a minor axis extending perpendicular to the major axis, the minor axis defining a second principal axis of the club head, the minor axis tilted at the non-zero angle relative to the vertical axis; wherein a moment of inertia of the club head about the major axis is greater than a moment of inertia of the club head about the horizontal axis; and wherein the club head further comprises: a first roll radius, and a second roll radius, the first roll radius smaller than the second roll radius.
 22. The club head of claim 21, further comprising: a loft line extending through the geometric center point, the loft line perpendicular to the ball striking face at the geometric center point; a center of gravity; a point of reference line extending through the center of gravity and the ball striking face, the point of reference line parallel to the loft line; and an intersection point of the point of reference line and the ball striking face; wherein the first roll radius is above the intersection point, and the second roll radius is below the intersection point.
 23. The club head of claim 21, wherein the majority comprises at least about 90 percent of a golfer's shots.
 24. The club head of claim 21, wherein the first major axis comprises a principal axis of the club head.
 25. The golf club head of claim 21, wherein the non-zero angle comprises between approximately 3.0 and 16.0 degrees.
 26. The golf club head of claim 21, wherein the first roll radius gives the ball striking face a rounded appearance when viewed from a side, and wherein the second roll radius gives the ball striking face a generally flattened appearance when viewed from the side. 